Looks like the most you are likely to get back is £1200
http://www.which.co.uk/consumer-rights/advice/the-airline-has-lost-or-damaged-my-bag-what-can-i-do
And expect a fight. They'll probably say you should have travel insurance to cover it.
I regularly carry £5K+ worth of camera gear as hand luggage and would never check it in, especially on a non direct flight. If an airline tried to make me put it in the hold, either at check-in or at the door of the plane then I tell them I will decline to board. This works quite well at the door of the plane, particularly if you already have hold baggage checked in. They have to off load it which almost always causes departure delays.
That's a great ploy! Although sadly I rarely travel with checked baggage which makes them more likely to call your bluff I suppose.
I was aware of the limit, and I do technically have insurance, although I will claim from the airline as a weapon of first resort and probably use insurer to cover the difference. I also intend to bill them for the day of my time that they wasted by lying to me (3 times) about the expected arrival time of my case. In fact, the €1200 will probably cover the
market value of the watch. Although obviously will not replace it.
As an aside, the first thing the customer service bod asked me was whether I had insurance and that he would advise me to claim on it if so. I (more calmly than I felt) explained that insurance was not relevant, I expected the airline to pay. This sort of thing really hacks me off and doesn't occur in any other sphere as far as I can tell. I mean, imagine if someone rear-ended you and then said "oh don't worry, you're fully comp, just claim on your own insurance"